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Numerical Methods For Convex Multistage Stochastic Optimization
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Book Synopsis Numerical Methods for Convex Multistage Stochastic Optimization by : Guanghui Lan
Download or read book Numerical Methods for Convex Multistage Stochastic Optimization written by Guanghui Lan and published by . This book was released on 2024-05-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). This monograph concentrates on SP and SOC modeling approaches. In these frameworks, there are natural situations when the considered problems are convex. The classical approach to sequential optimization is based on dynamic programming. It has the problem of the so-called "curse of dimensionality", in that its computational complexity increases exponentially with respect to the dimension of state variables. Recent progress in solving convex multistage stochastic problems is based on cutting plane approximations of the cost-to-go (value) functions of dynamic programming equations. Cutting plane type algorithms in dynamical settings is one of the main topics of this monograph. Also discussed in this work are stochastic approximation type methods applied to multistage stochastic optimization problems. From the computational complexity point of view, these two types of methods seem to be complimentary to each other. Cutting plane type methods can handle multistage problems with a large number of stages but a relatively smaller number of state (decision) variables. On the other hand, stochastic approximation type methods can only deal with a small number of stages but a large number of decision variables.
Book Synopsis Lectures on Stochastic Programming by : Alexander Shapiro
Download or read book Lectures on Stochastic Programming written by Alexander Shapiro and published by SIAM. This book was released on 2009-01-01 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.
Book Synopsis Generalized Bounds for Convex Multistage Stochastic Programs by : Daniel Kuhn
Download or read book Generalized Bounds for Convex Multistage Stochastic Programs written by Daniel Kuhn and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work was completed during my tenure as a scientific assistant and d- toral student at the Institute for Operations Research at the University of St. Gallen. During that time, I was involved in several industry projects in the field of power management, on the occasion of which I was repeatedly c- fronted with complex decision problems under uncertainty. Although usually hard to solve, I quickly learned to appreciate the benefit of stochastic progr- ming models and developed a strong interest in their theoretical properties. Motivated both by practical questions and theoretical concerns, I became p- ticularly interested in the art of finding tight bounds on the optimal value of a given model. The present work attempts to make a contribution to this important branch of stochastic optimization theory. In particular, it aims at extending some classical bounding methods to broader problem classes of practical relevance. This book was accepted as a doctoral thesis by the University of St. Gallen in June 2004.1 am particularly indebted to Prof. Dr. Karl Frauendorfer for - pervising my work. I am grateful for his kind support in many respects and the generous freedom I received to pursue my own ideas in research. My gratitude also goes to Prof. Dr. Georg Pflug, who agreed to co-chair the dissertation committee. With pleasure I express my appreciation for his encouragement and continuing interest in my work.
Book Synopsis Numerical Techniques for Stochastic Optimization by : I︠U︡riĭ Mikhaĭlovich Ermolʹev
Download or read book Numerical Techniques for Stochastic Optimization written by I︠U︡riĭ Mikhaĭlovich Ermolʹev and published by Springer. This book was released on 1988 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Optimization by : Kurt Marti
Download or read book Stochastic Optimization written by Kurt Marti and published by Springer. This book was released on 1992 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis First-order and Stochastic Optimization Methods for Machine Learning by : Guanghui Lan
Download or read book First-order and Stochastic Optimization Methods for Machine Learning written by Guanghui Lan and published by Springer Nature. This book was released on 2020-05-15 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.
Book Synopsis Systems Optimization Methodology by : V. V. Kolbin
Download or read book Systems Optimization Methodology written by V. V. Kolbin and published by World Scientific. This book was released on 1999 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with theoretical fundamentals and numerical methods of optimizing nondetermined models of systems. The main body of this work is devoted to investigation and optimization of system models under incomplete information. Much consideration is given to one-, two- and multistage problems of stochastic programming, solution methods and problems of solution stability. Optimization problems with fuzzy variables and optimization problems in function spaces are investigated. Examples are given for implementation of specific models of optimization under incomplete information. The book is based on lectures delivered by the author since 1965 for undergraduates and postgraduates at St. Petersburg (Leningrad) State University.
Book Synopsis Multistage Stochastic Optimization by : Georg Ch. Pflug
Download or read book Multistage Stochastic Optimization written by Georg Ch. Pflug and published by Springer. This book was released on 2014-11-12 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book.
Book Synopsis Stochastic Multi-Stage Optimization by : Pierre Carpentier
Download or read book Stochastic Multi-Stage Optimization written by Pierre Carpentier and published by Springer. This book was released on 2015-05-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.
Book Synopsis Dynamic Stochastic Optimization by : Kurt Marti
Download or read book Dynamic Stochastic Optimization written by Kurt Marti and published by Springer Science & Business Media. This book was released on 2004 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume considers optimal stochastic decision processes from the viewpoint of stochastic programming. It focuses on theoretical properties and on approximate or numerical solution techniques for time-dependent optimization problems with random parameters (multistage stochastic programs, optimal stochastic decision processes). Methods for finding approximate solutions of probabilistic and expected cost based deterministic substitute problems are presented. Besides theoretical and numerical considerations, the proceedings volume contains selected refereed papers on many practical applications to economics and engineering: risk, risk management, portfolio management, finance, insurance-matters and control of robots.
Book Synopsis Stability, Approximation, and Decomposition in Two- and Multistage Stochastic Programming by : Christian Küchler
Download or read book Stability, Approximation, and Decomposition in Two- and Multistage Stochastic Programming written by Christian Küchler and published by Springer Science & Business Media. This book was released on 2010-05-30 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Christian Küchler studies various aspects of the stability of stochastic optimization problems as well as approximation and decomposition methods in stochastic programming. In particular, the author presents an extension of the Nested Benders decomposition algorithm related to the concept of recombining scenario trees.
Book Synopsis Stochastic Optimization Methods by : Kurt Marti
Download or read book Stochastic Optimization Methods written by Kurt Marti and published by Springer Science & Business Media. This book was released on 2005 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a concise overview of stochastic optimization and considers nonlinear optimization problems. Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems.
Book Synopsis Convex and Stochastic Optimization by : J. Frédéric Bonnans
Download or read book Convex and Stochastic Optimization written by J. Frédéric Bonnans and published by Springer. This book was released on 2019-04-24 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to convex duality for optimization problems in Banach spaces, integration theory, and their application to stochastic programming problems in a static or dynamic setting. It introduces and analyses the main algorithms for stochastic programs, while the theoretical aspects are carefully dealt with. The reader is shown how these tools can be applied to various fields, including approximation theory, semidefinite and second-order cone programming and linear decision rules. This textbook is recommended for students, engineers and researchers who are willing to take a rigorous approach to the mathematics involved in the application of duality theory to optimization with uncertainty.
Book Synopsis Stochastic Programming Methods and Technical Applications by : Kurt Marti
Download or read book Stochastic Programming Methods and Technical Applications written by Kurt Marti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems arising in practice usually contain several random parameters. Hence, in order to obtain optimal solutions being robust with respect to random parameter variations, the mostly available statistical information about the random parameters should be considered already at the planning phase. The original problem with random parameters must be replaced by an appropriate deterministic substitute problem, and efficient numerical solution or approximation techniques have to be developed for those problems. This proceedings volume contains a selection of papers on modelling techniques, approximation methods, numerical solution procedures for stochastic optimization problems and applications to the reliability-based optimization of concrete technical or economic systems.
Book Synopsis Continuous Optimization by : V. Jeyakumar
Download or read book Continuous Optimization written by V. Jeyakumar and published by Springer Science & Business Media. This book was released on 2005-08-10 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The search for the best possible performance is inherent in human nature. Individuals, enterprises and governments all seek optimal—that is, the best—possible solutions of problems that they meet. Evidently, continuous optimization plays an increasingly significant role in everyday management and technical decisions in science, engineering and commerce. The collection of 16 refereed papers in this book covers a diverse number of topics and provides a good picture of recent research in continuous optimization. The first part of the book presents substantive survey articles in a number of important topic areas of continuous optimization. Most of the papers in the second part present results on the theoretical aspects as well as numerical methods of continuous optimization. The papers in the third part are mainly concerned with applications of continuous optimization. Hence, the book will be an additional valuable source of information to faculty, students, and researchers who use continuous optimization to model and solve problems. Audience This book is intended for researchers in mathematical programming, optimization and operations research; engineers in various fields; and graduate students in applied mathematics, engineering and operations research.
Book Synopsis Lectures on Stochastic Programming: Modeling and Theory, Third Edition by : Alexander Shapiro
Download or read book Lectures on Stochastic Programming: Modeling and Theory, Third Edition written by Alexander Shapiro and published by SIAM. This book was released on 2021-08-19 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and rigorous presentation of contemporary models and ideas of stochastic programming, this book focuses on optimization problems involving uncertain parameters for which stochastic models are available. Since these problems occur in vast, diverse areas of science and engineering, there is much interest in rigorous ways of formulating, analyzing, and solving them. This substantially revised edition presents a modern theory of stochastic programming, including expanded and detailed coverage of sample complexity, risk measures, and distributionally robust optimization. It adds two new chapters that provide readers with a solid understanding of emerging topics; updates Chapter 6 to now include a detailed discussion of the interchangeability principle for risk measures; and presents new material on formulation and numerical approaches to solving periodical multistage stochastic programs. Lectures on Stochastic Programming: Modeling and Theory, Third Edition is written for researchers and graduate students working on theory and applications of optimization, with the hope that it will encourage them to apply stochastic programming models and undertake further studies of this fascinating and rapidly developing area.
Book Synopsis Systems Optimization Methodology: Part Ii by : Vyacheslav V Kolbin
Download or read book Systems Optimization Methodology: Part Ii written by Vyacheslav V Kolbin and published by World Scientific. This book was released on 1999-03-26 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with theoretical fundamentals and numerical methods of optimizing nondetermined models of systems. The main body of this work is devoted to investigation and optimization of system models under incomplete information. Much consideration is given to one-, two- and multistage problems of stochastic programming, solution methods and problems of solution stability. Optimization problems with fuzzy variables and optimization problems in function spaces are investigated. Examples are given for implementation of specific models of optimization under incomplete information.The book is based on lectures delivered by the author since 1965 for undergraduates and postgraduates at St. Petersburg (Leningrad) State University.
